If you're right handed but like kenkayotsu grips with left leg in front, left leg uchi mata must work pretty great for you. I was thinking in terms of standing in an orthodox boxing stance with your opponent also standing orthodox, you're in great position for left lead o soto gari. But I suppose it depends on what stance your opponent takes and indeed if he allows you to take kenkayotsu grips vs. mirroring you for aiyotsu in gi.
I started wrestling before Judo (but had already started boxing orthodox), and the biggest driver for throws was guys taking a collar tie on me with their right hand. So being right handed myself, I'd do the same tie up on them. And from there I'd go for duck unders and arm drags on their right arm and also head and arm throw/koshi guruma also from the right side. And the collar tie in wrestling being pretty analogous to aiyotsu grips in Judo, I starting doing that also with right hand on the lapel, also driven by other guy almost always taking the same grips on me.
But it is an interesting question and one I've thought about a lot. With all the different stances I've gotten used to taking in different rulesets, going for TDs from the feet, I'm now used to standing square to my opponent in more of a defensive stance, while alternately circling right or left. If I circle left, it feels like stepping into an orthodox jab and I go for a high head inside single leg, which is still pretty much the only left side TD I have any success with. If I circle right, I'm going for right side Judo throws, hane goshi, de ashi harai, koshi guruma, tani otoshi, tai otoshi, o uchi gari, ko uchi gake. But having tried and failed miserably at using more left-side Judo throws against resisting opponents, it's an aspect of my TD game that needs a lot of work.